Not only Pinki but also her friends _________ buying books.

• is
• has
• have
• are
Correct Option: D  [ are ]

Remark:

Neither John nor Alex __________ scored the century.

• have
• was
• has
• is
Correct Option: C  [ has ]

Remark: in case "Neither-Nor" the verb must agree with the second subject (the subject closer to the verb).

Neither the books nor the magazine ________ on the shelf.

• were
• have
• have been
• was
Correct Option: D  [ was ]

Remark: The verb agrees with the closer part of the subject, which is "magazine" in this case. Here "Magazine" is singular subject, so "was" used.

The boy in the bus ________ like your brother.

• look
• looks
• looking
• have been looked
Correct Option: B  [ looks ]

Remark:

The Moon _______ around the Earth

• move
• moving
• moved
• moves
Correct Option: D  [ moves ]

Remark: Subject is "Moon" a Singular noun, go with singular verb.
When universal truths are mentioned, the verb used should be the simple present tense.

Neither of the two stores _________ open.

• are
• is
• has
• have
Correct Option: B  [ is ]

Remark: Sentence begins with "neither" or "either" without the "or/nor" combination, the verb is singular.

Everyone ___ happy with the results.

• is
• are
• have
• has
Correct Option: A  [ is ]

Remark: "Everyone" is a singular indefinite pronoun, so it takes a singular verb.

The team _______ playing well.

• have
• were
• is
• are
Correct Option: C  [ is ]

Remark: "team" is a collective noun and should be treated as a singular entity. Therefore, the verb "is" (singular) used.

Mathematics ___ my favorite subject.

• are
• is
• were
• has
Correct Option: B  [ is ]

Remark: "Mathematics" is treated as a singular subject even though it ends in "s".

Not only my parents but also I _______ regretting the change of school.

• are
• is
• am
• No option is appropriate
Correct Option: C  [ am ]

Remark: in case "Not only...but also" the verb should agree with the subject closest to the verb.